Infinite-dimensional stochastic differential equations arising from Airy random point fields

We identify infinite-dimensional stochastic differential equations (ISDEs) describing the stochastic dynamics related to Airy$_{\beta }$ random point fields with $\beta =1,2,4$. We prove the existence of unique strong solutions of these ISDEs. When $\beta = 2$, this solution is equal to the stochastic dynamics defined by the space-time correlation functions obtained by Spohn and Johansson among others. We develop a new method to construct a unique, strong solution of ISDEs. We expect that our approach is valid for other soft-edge scaling limits of stochastic dynamics arising from the random matrix theory.Comment: 55 page

Cores of Dirichlet forms related to random matrix theory

We prove the sets of polynomials on configuration spaces are cores of Dirichlet forms describing interacting Brownian motion in infinite dimensions. Typical examples of these stochastic dynamics are Dyson's Brownian motion and Airy interacting Brownian motion. Both particle systems have logarithmic interaction potentials, and naturally arise from random matrix theory. The results of the present paper will be used in a forth coming paper to prove the identity of the infinite-dimensional stochastic dynamics related to the random matrix theories constructed by apparently different methods: the method of space-time correlation functions and that of stochastic analysis.Comment: 6 pages, revised version, published in PJA in 201

Interaction of fcc-Palladium nano-crystals with Hydrogen during PECVD growth of Carbon nanotubes

Using plasma-enhanced chemical vapor deposition (PECVD) with Acetylene and Ammoniac on Pd-specimens Carbon nanotubes (CNT) could be produced successfully. Two different devices are compared and the conditions for best growth conditions are explained. The detailed analysis of electron diffraction pattern obtained by transmissions electron microscopy (TEM) of as-grown specimen showed an expansion of the Pd lattice, which can be explained by the formation of fcc-PdHx for x=0...1. For x=1..2 the first investigation of hexagonal -PdH2 is reported, which lattice spacing is independent on the hydrogen content. The amount of fcc-PdH and hcp-PdH2 increases when the specimens are treated subsequently with Hydrogen. A growth model is provided.Comment: 6 pages, 6 figure

Stochastic differential equations for infinite particle systems of jump type with long range interactions

Infinite-dimensional stochastic differential equations (ISDEs) describing systems with an infinite number of particles are considered. Each particle undergoes a L\'evy process, and the interaction between particles is determined by the long-range interaction potential. The potential is of Ruelle's class or logarithmic. We discuss the existence and uniqueness of strong solutions of the ISDEs.Comment: 60page